What it the measure of the tangent-chord angle when a circle is divided into three arcs in the ratio of 2 3 4 with the tangent-chord intercepting the smallest of the three arcs?

Answer 1

An angle formed by a tangent and a chord is measured by one-half its intercepted arc.

Let x = unit part, so that our angle measure is x degrees (2x/2).

Since there are 360 degrees in a circle, then

2x + 3x + 4x = 360

9x = 360

x = 40 (answer)